Symmetric heat and mass transfer in a rotating spherical layer

Старченко, С. В.; Kotelnikova, M. S.

doi:10.1134/1.1469144

Cited by 5 publications

(17 citation statements)

References 14 publications

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“…Figs. 1 and 2 show the spherically symmetric parts of n and S (physical parameters used for calculations (see Table 1) correspond to previous studies [8,9,16]). An increase in the convective velocity U leads to a decrease of perturbations of the light constituent mass fraction and specific entropy.…”

Section: Spherically Symmetric Solution With Convectionmentioning

confidence: 86%

“…Let us describe convective motions in the Earth's outer core as a perturbation of the reference state in the form S þ S; n þ n; p þ p; V (variables without the bar designate these perturbations). The governing equations for perturbations in a frame of reference rotating at constant angular velocity X have the form [2,16] rð qVÞ ¼ 0;…”

Section: The Governing Equationsmentioning

confidence: 99%

“…(6). Note that expressions (17) and (18) are independent of time if _ n; _ S; n CMB ; S CMB and q S are constants [2,8,9,16,17].…”

Section: Spherically Symmetric Solution With Convectionmentioning

confidence: 99%

“…Let us especially emphasize that expression (16) represents an approximation of the fluid velocity in the FOC except those regions where horizontal flows become comparable with vertical flows. Although we do not consider the hydrodynamics in these boundary layers, expressions (17) and (18) lead to an adequate physical behavior of obtained solutions near the CMB.…”

Section: Spherically Symmetric Solution With Convectionmentioning

confidence: 99%

“…An attempt to find an exact spherically symmetric analytic solution of this problem is presented by Starchenko and Kotel'nikova [16]. Further their solution was corrected in [17].…”

Section: Introductionmentioning

confidence: 99%

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Mathematical modeling of solidification process near the inner core boundary of the Earth

Alexandrov

Malygin

2013

Applied Mathematical Modelling

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a b s t r a c tRadially symmetric analytic solutions of the heat and mass transfer equations governing convection in the Earth's fluid core are found in terms of deviations from the adiabatic reference state. We demonstrate that an increase of the convective velocity leads to a decrease of the light constituent mass fraction and specific entropy. Where fluid is rising/descending, convective motions decrease/increase the mass fraction and entropy at the inner core boundary (ICB). The influence of convective motions on the thermal fluxes at the core mantle boundary is studied. On the basis of exact solutions we demonstrate that the liquid is supercooled near the ICB. An important point is that an increase in the convective velocity directed to the ICB increases the constitutional supercooling. We show that the anelastic model (AM) can be used only at small supercoolings near the ICB. The most probable solidification scenario ''constitutional supercooling and morphological instability'' should be described by a mushy layer theory near the ICB and by the AM in the rest region of the fluid outer core. On the basis of dendritic theory and selection mechanisms of crystal growth the dendrite tip radius and interdendritic spacing in the mushy layer at the ICB are determined in the presence of convection.

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Section: Spherically Symmetric Solution With Convectionmentioning

confidence: 86%

Section: The Governing Equationsmentioning

confidence: 99%

“…(6). Note that expressions (17) and (18) are independent of time if _ n; _ S; n CMB ; S CMB and q S are constants [2,8,9,16,17].…”

Section: Spherically Symmetric Solution With Convectionmentioning

confidence: 99%

Section: Spherically Symmetric Solution With Convectionmentioning

confidence: 99%

“…An attempt to find an exact spherically symmetric analytic solution of this problem is presented by Starchenko and Kotel'nikova [16]. Further their solution was corrected in [17].…”

Section: Introductionmentioning

confidence: 99%

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